Correlation And Regression

Created By :-Shrayas.sWesley.V

Tahir hussain Qureshi

CORRELATION

• When we have data on only one variable we can find arithmetic mean , median , mode or variance of the variable.

• By saying that marks scored by students at s.s.c. and h.s.c. are related is not sufficient to measure degree of relationship.

CORRELATION

To measure the degree of relationship we have following measure:

1. Scatter diagram method2. Co-variance method3. Karl-pearson’s coefficient of

correlation4. Spearman’s rank correlation

coefficient.

Scatter Diagram

• A scatter diagram is used for analyzing relationships between two variables graphically . One variable is plotted on the horizontal axis and the other is plotted on the vertical axis.

• Types of Scatter diagram :1. Perfect positive correlation 2. Positive correlation3. Negative correlation4. Perfect negative correlation

Perfect Positive correlation

Positive correlation

Negative correlation

Perfect negative correlation

Covariance method

• If(x1,y1),(x2,y2),........(xn,yn) are n observation on bivariate data then covariance between two variables is defined as

Using covariance the realtion between x and y is interpreted as under.if cov(x,y)<0 then there is negative correlation between x and y. If cov(x,y)=0 then there is no linear relationship nbetween x and y. If cov(x,y)>0 then there is positive correlation between x and y.

KARL PEARSON’S COEFFICIENT

• If (xi,yi),i=1,2,....n are n pairs of observations on bivariate data then Karl Pearson’s coefficient of correlation between x and y is given by:

Spearman’s rank correlation

• If (xi,yi),i=1,2,....n are n observation in bivariate data and Rx denotes the rank of X observation and Ry denotes the rank of Y observations then define d=Rx-Ry.

• Rank correlation coefficient between x and y is

Regression

• Regression gives the functional relationship between two variables

Regression means estimate value of one variable when value of other correlated variable are known.

Thus to estimate y, for given x, y is dependent and x is independent

variable. whereas to estimate x for given y, x is dependent and y is independent

variable.

Accordingly we have two regression equation :

1)Regression equation of y on x 2) Regression equation of x on y

Regression equation of y on x

Here y is dependent variable and x is independent variable.

And we denote By :-

Regression equation of x on y :-

Here y is dependent variable and x is independent variable.

And we denote By :-